This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A356539 #11 Aug 11 2022 08:54:12 %S A356539 1,5,12,49,86,492,736,3977,8757,34030,59060,384924,531454,2672528, %T A356539 6672552,26093113,43046738,261646137,387420508,2181624374,4682526672, %U A356539 17435870644,31381059632,204908769276,299863458511,1412168408630,3392641222200,13912336721584 %N A356539 a(n) = Sum_{d|n} d * 3^(n-d). %F A356539 G.f.: Sum_{k>=1} k * x^k/(1 - (3 * x)^k). %F A356539 If p is prime, a(p) = p + 3^(p-1). %t A356539 a[n_] := DivisorSum[n, # * 3^(n - #) &]; Array[a, 30] (* _Amiram Eldar_, Aug 11 2022 *) %o A356539 (PARI) a(n) = sumdiv(n, d, d*3^(n-d)); %o A356539 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1-(3*x)^k))) %Y A356539 Cf. A090879, A342675, A356540. %K A356539 nonn %O A356539 1,2 %A A356539 _Seiichi Manyama_, Aug 11 2022